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Defusing Bertrand's Paradox

Gyenis, Zalán and Miklós, Rédei (2012) Defusing Bertrand's Paradox. In: [2012] Seventh Quadrennial Fellows Conference of the Center for Philosophy of Science (12-14 June 2012; Mugla, Turkey).

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    Abstract

    The classical interpretation of probability together with the Principle of Indifference are formulated in terms of probability measure spaces in which the probability is given by the Haar measure. A notion called Labeling Irrelevance is defined in the category of Haar probability spaces, it is shown that Labeling Irrelevance is violated and Bertrand's Paradox is interpreted as the very proof of violation of Labeling Invariance. It is shown that Bangu's attempt (Bangu 2010) to block the emergence of Bertrand's Paradox by requiring the re-labeling of random events to preserve randomness cannot succeed non-trivially. A non-trivial strategy to preserve Labeling Irrelevance is identified and it is argued that, under the interpretation of Bertrand's Paradox suggested in the paper, the paradox does not undermine either the Principle of Indifference or the classical interpretation and is in complete harmony with how mathematical probability theory is used in the sciences to model phenomena. It also is argued however that the content of the Principle of Indifference cannot be specified in such a way that it can establish the classical interpretation of probability as descriptively accurate, predictively successful or rational.


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    Item Type: Conference or Workshop Item (UNSPECIFIED)
    Additional Information: Paper delivered to the 7th Quadrennial International Fellows Conference, Mugla, Turkey, June 14, 2012
    Keywords: Bertrand's Paradox, Principle of Indifference, interpretation of probability, Haar measure
    Subjects: Specific Sciences > Probability/Statistics
    Conferences and Volumes: [2012] Seventh Quadrennial Fellows Conference of the Center for Philosophy of Science (12-14 June 2012; Mugla, Turkey)
    Depositing User: Dr Miklos Redei
    Date Deposited: 03 Jul 2012 12:05
    Last Modified: 20 Jan 2013 09:08
    Item ID: 9200
    URI: http://philsci-archive.pitt.edu/id/eprint/9200

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